Journal of Statistical Physics, Vol. 56, Nos. 3/4, 1989. p. 437-459.
We investigate the dynamics of a random walk in a random multiplicative medium. This results in a random, but correlated, multiplicative process for the spatial distribution of random walkers. We show how the details of these correlations determine the asymptotic properties of the walk, i.e., the central limit theorem does not apply to these multiplicative processes. We also study a periodic source-trap medium in which a unit cell contains one source, followed by L- 1 traps. We calculate the asymptotic behavior of the number of particles,
and determine the conditions for which there is growth or decay in this average number. Finally, we discuss the asymptotic behavior of a random walk in the presence of randomly distributed, partially-absoprbing traps...